New criteria for the principle of information causality

Author(s)

Lucas da Silva Pollyceno

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2021-04-09

Examining board members

Rafael Luiz da Silva Rabelo; Rafael Chaves Souto Araújo; Marcos César de Oliveira

• Advisor: Rafael Luiz da Silva Rabelo

Abstract

Quantum mechanics is fundamentally defined by means of its mathematical formalism: Hilbert spaces, wave functions, operators. In contrast, other physical theories, such as special relativity, can be formulated by means of physical principles. One of the most important problems in the foundations of quantum mechanics is, thus, the search for a physical principle that should be capable of highlighting quantum mechanics from more general probabilistic theories. To that purpose, several principles have been proposed recently, among which is the principle of information causality. Roughly speaking, this principle states the following: if a party, Alice, sends a message to another party, Bob, the potential gain of information of Bob is limited by the information content of the message, even when nonlocal resources, such as entangled quantum states, are allowed. It has been showed that quantum mechanics obeys the principle of information causality, however, it is not known if all theories that allow supra-quantum resources violate it, mostly due to the difficulty of finding mathematical criteria that formalize the idea behind the principle. Recently, a new approach, which combines causality theory, classical information theory and convex geometry, has been proposed as a powerful tool to find such criteria. In this dissertation, we study in detail the formulation about the principle of information causality. In this way, we present its mathematical and conceptual formulation, as well as the mathematical theory related to the most recent informational-geometric approach. Furthermore, we investigate some open questions within this context and apply this new informational approach in order to formulate new mathematical criteria for the principle of information causality in new scenarios and to investigate how this criterion is capable of excluding supra-quantum non-local theories. (AU)

• FAPESP's process: 19/00451-9 - New criteria for the information causality principle
• Grantee: Lucas da Silva Pollyceno
• Support Opportunities: Scholarships in Brazil - Master